Abstract Model calibration for radioactive contaminant transport in fractured rock has been formulated as an inverse problem and a solution proposed using a Bayesian approach. In particular, Markov random field (MRF) models have been proposed as a priori distribution functions for fracture apertures. The fracture reconstruction is based on the a posteriori distribution function simulation using a Markov chain Monte Carlo procedure. A two-level estimation-reconstruction algorithm has been developed. On the first level, the fracture apertures are reconstructed using simulated annealing (SA), with the Metropolis-Hastings dynamics. The MRF parameters are assumed known. On the second level, after several sweeps of the entire field using SA, the MRF parameters are updated using the method of pseudolikelihood. The competing models are finally compared using an asymptotic form of the Bayes factor.